Evaluation of the convolution sums ∑l + 6 m = n σ (l) σ (m) and ∑2 l + 3 m = n σ (l) σ (m)

The sums ∑(l, m) ∈ N2, l + 6 m = n σ (l) σ (m) and ∑(l, m) ∈ N2, 2 l + 3 m = n σ (l) σ (m) are evaluated for all n ∈ N, and their evaluations used to determine the number of representations of a positive integer n by the form{Mathematical expression}.

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